There are numerous situations in which the location of an aircraft's center of gravity has an effect on the manner in which the aircraft control surfaces are operated to maneuver the aircraft. One situation in which locating the aircraft's center of gravity is important is during the final stages of an automatic landing procedure. When a large aircraft nears the ground, the aircraft experiences substantial lift and pitching moment changes. To compensate for these moment changes, open loop ground effect compensation is typically incorporated in modern autoland systems. The ground effect compensation causes the aircraft to execute a flare-like maneuver prior to touchdown of the aircraft. The amount of compensation provided to the elevators of an aircraft in order to execute the flare maneuver primarily depends on the aircraft approach speed, the flap setting being used during the landing procedure, and the location of the aircraft's center of gravity. Accurately estimating an aircraft's center of gravity during flight therefore improves the overall touchdown capability of the aircraft. It will also be recognized that there are numerous other situations in which an aircraft center of gravity estimate is a useful input to the flight control system in order to implement various flight control laws. To generally improve the handling of aircraft, it is therefore very beneficial to be able to provide a real time estimate of an aircraft center of gravity.
Historically, it was impossible to provide a real time measurement of an aircraft's center of gravity using onboard equipment. In practice, it had therefore been accepted to use a worst case estimate of the center of gravity in automatic flight control situations in which the center of gravity was an important parameter. Although the practice of using a worst case estimate provided generally satisfactory results, improved performance could be achieved if the center of gravity could be accurately estimated during flight.
A technique for providing a real time estimate of an aircraft's center of gravity was first disclosed in U.S. Pat. No. 5,034,896, entitled "Method and Apparatus for Real Time Estimation of Aircraft Center of Gravity" (expressly incorporated herein by reference). The '896 patent disclosed a graphical technique to estimate the center of gravity of an aircraft based on an aircraft's angle of attack, flap setting, and stabilizer position. In the estimation technique, a CG estimator estimates the center of gravity from the equation A.sub.1 S+A.sub.2, where S is equal to the stabilizer position of the aircraft, and A.sub.1 and A.sub.2 are dependent upon the aircraft flap setting and the aircraft angle of attack at the time that the center of gravity estimate is being provided. The variable A.sub.1 is generated by a slope generator which determines the slope from a slope relationship graph. The slope is based on the aircraft angle of attack and aircraft flap setting. The variable A.sub.2 is generated by an intercept generator, which also receives the aircraft's angle of attack and flap setting and determines the intercept value from an intercept relationship graph. A summer adds the results from the intercept generator with the results from the slope generator multiplied by the stabilizer position in order to arrive at a center of gravity estimate. The center of gravity estimate is used by an elevator controller to generate an appropriate elevator compensation signal.
While the center of gravity estimator disclosed in the '896 patent was an improvement over the method of using the worst case estimate of the center of gravity, several shortcomings existed in the method. Measurements made during landing simulations indicate that a graph of the airplane stabilizer position versus the angle of attack for a given center of gravity should exhibit a weak convex nonlinearity. When plotting stabilizer position versus angle of attack for a given center of gravity estimated using the method of the '896 patent, however, the graph exhibits a weak concave nonlinearivy, especially for an angle of attack within a range of 3.degree. to 6.degree.. Consequently, within the mid-range angle of attack, the center of gravity estimator of the '896 patent produces an error of as much as 4% of the mean aerodynamic chord (MAC) in comparison with the actual location of the airplane's center of gravity. Moreover, the method and apparatus disclosed in the '896 patent is rather cumbersome and difficult to implement in flight control system. Because the method relies on graphical techniques to determine an aircraft's center of gravity, the method is difficult to implement with limited computing resources. It would therefore be an improvement over those techniques known in the art to generate a real time estimate of an aircraft's center of gravity that is highly accurate and easier to implement in the flight control system.